Chad was asked whether the following equation is an identity:
2 answers:
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A. The perimeter of quadrilaterals are same when x=2.
B. The area of quadrilaterals are same when x=4.6
<u>Step-by-step explanation</u>:
A. <u>Perimeter of the quadrilaterals must be equal.</u>
- Perimeter of square is 4a.
- where, a = 6
- Perimeter of rectangle is 2(l+b).
- where, l = 2 and b = (3x+4)
Perimeter of square = Perimeter of rectangle
4(6) = 2(2+3x+4)
⇒ 24 = 2(3x+6)
⇒ 24 = 6x + 12
⇒ 6x = 12
⇒ x = 12/6
x = 2
For x=2, the perimeters of both the quadrilaterals are same.
B. <u>Area of the quadrilaterals must be equal.</u>
- Area of square is a².
- where, a = 6.
- Area of rectangle is l
b.
- where, l = 2 and b = (3x+4)
Area of square = Area of rectangle
(6)² = 2(3x+4)
36 = 6x+8
6x = 28
x = 28/6
x = 4.6
For x=4.6, the area of both the quadrilaterals are same.